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运筹学学报 >

2016 , Vol. 20 >Issue 1: 125 - 130

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2016.01.013

运筹学

关于分数k-因子临界图与分数k-可扩图的若干结果

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  • 1. 华南师范大学数学科学学院, 广州 510631

收稿日期: 2015-05-28

  网络出版日期: 2016-03-15

基金资助

国家自然科学基金(No. 11551003), 广州市科技计划项目科学研究专项基金(No. 201510010265)

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Some results on fractional k-factor-critical graphs and fractional k-extendable graphs

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  • 1.  School of Mathematical Science, South China Normal University, Guangzhou 510631, China

Received date: 2015-05-28

  Online published: 2016-03-15

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摘要

一个简单图G, 如果对于V(G)的任意k元子集S, 子图G-S都包含分数完美匹配, 那么称G为分数k-因子临界图. 如果图G的每个k-匹配M都包含在一个分数完美匹配中, 那么称图G为分数k-可扩图. 给出一个图是分数k-因子临界图和分数k-可扩图的充分条件, 并给出一个图是分数k-因子临界图的充分必要条件.

关键词： 分数完美匹配; 分数k-因子临界的; 分数k-可扩的; 分数匹配数

本文引用格式

黄晓娴, 刘岩, 吴博思 . 关于分数k-因子临界图与分数k-可扩图的若干结果[J]. 运筹学学报, 2016 , 20(1) : 125 -130 . DOI: 10.15960/j.cnki.issn.1007-6093.2016.01.013

Abstract

 A simple graph G is said to be fractional k-factor-critical if after deleting any k vertices, the remaining subgraph still has a fractional perfect matching. A graph G is called a fractional k-extendable graph if G has a fractional perfect matching containing M for any k-matching M. In this paper, a sufficient condition for a graph to be fractional k-factor-critical graph and fractional k-extendable graph is given, respectively. Besides, a sufficient and necessary condition for a graph to be fractional k-factor-critical graph is given.

Key words： fractional perfect matching; fractional k-factor-critical; fractional k-extendable; fractional matching number

参考文献

[1] 李巧, 刘岩. 分数k-因子临界图的条件 [J]. 运筹学学报, 2013, 17(4): 123-130.
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[7] Qi F. The study of fractional (k,n)-critical graphs and the correlative properties [D]. Jinan: Shandong Normal University, 2008.

 
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